We study how an imposed fluid flow - laminar or turbulent - modifies the transport properties of inertial particles, namely their terminal velocity, effective diffusivity, and concentration following a point-source emission. Such quantities are investigated by means of analytical and numerical computations, as functions of the control parameters of both flow and particle, i.e. density ratio, inertia, Brownian diffusivity, gravity (or other external forces), turbulence intensity, compressibility degree, space dimension, and geometric\temporal properties. The complex interplay between these parameters leads to the following conclusion of interest in the realm of applications: any attempt to model dispersion and sedimentation processes (or, equivalently, the wind-driven surface transport of floaters) cannot avoid taking into account the full details of the flow field and of the inertial particle.